Worst-case analysis based adaptive control design for SISO linear systems with plant and actuation uncertainties

We study the adaptive controller design for SISO linear systems subjected to plant and actuation uncertainties simultaneously. We first formulate the actuation and plant components of the linear system as two subsystems sequentially interconnected with additional feedback, and then convert the robust adaptive control problem as a nonlinear H∞control problem under imperfect state measurement. We derive the estimators and identifiers of the two subsystems using cost-to-come analysis, and then apply integrator backstepping methodology to obtain the control law. The controller guarantees the boundedness of closed-loop signals with bounded exogenous disturbances, and achieves desired disturbance attenuation level with respect to the unmeasured exogenous disturbance inputs and arbitrary positive or zero disturbance attenuation level with respect to the measured disturbance inputs. In addition, for the measured disturbances that the controller can achieve zero disturbance attenuation level, the asymptotic tracking objective is achieved even if they are only uniformly bounded without being of finite energy.